1 /*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17
18 package org.apache.commons.math4.legacy.ode.events;
19
20 import org.apache.commons.math4.legacy.analysis.UnivariateFunction;
21 import org.apache.commons.math4.legacy.analysis.solvers.AllowedSolution;
22 import org.apache.commons.math4.legacy.analysis.solvers.BracketedUnivariateSolver;
23 import org.apache.commons.math4.legacy.analysis.solvers.PegasusSolver;
24 import org.apache.commons.math4.legacy.analysis.solvers.UnivariateSolver;
25 import org.apache.commons.math4.legacy.analysis.solvers.UnivariateSolverUtils;
26 import org.apache.commons.math4.legacy.exception.MaxCountExceededException;
27 import org.apache.commons.math4.legacy.exception.NoBracketingException;
28 import org.apache.commons.math4.legacy.ode.EquationsMapper;
29 import org.apache.commons.math4.legacy.ode.ExpandableStatefulODE;
30 import org.apache.commons.math4.legacy.ode.sampling.StepInterpolator;
31 import org.apache.commons.math4.core.jdkmath.JdkMath;
32
33 /** This class handles the state for one {@link EventHandler
34 * event handler} during integration steps.
35 *
36 * <p>Each time the integrator proposes a step, the event handler
37 * switching function should be checked. This class handles the state
38 * of one handler during one integration step, with references to the
39 * state at the end of the preceding step. This information is used to
40 * decide if the handler should trigger an event or not during the
41 * proposed step.</p>
42 *
43 * @since 1.2
44 */
45 public class EventState {
46
47 /** Event handler. */
48 private final EventHandler handler;
49
50 /** Maximal time interval between events handler checks. */
51 private final double maxCheckInterval;
52
53 /** Convergence threshold for event localization. */
54 private final double convergence;
55
56 /** Upper limit in the iteration count for event localization. */
57 private final int maxIterationCount;
58
59 /** Equation being integrated. */
60 private ExpandableStatefulODE expandable;
61
62 /** Time at the beginning of the step. */
63 private double t0;
64
65 /** Value of the events handler at the beginning of the step. */
66 private double g0;
67
68 /** Simulated sign of g0 (we cheat when crossing events). */
69 private boolean g0Positive;
70
71 /** Indicator of event expected during the step. */
72 private boolean pendingEvent;
73
74 /** Occurrence time of the pending event. */
75 private double pendingEventTime;
76
77 /** Occurrence time of the previous event. */
78 private double previousEventTime;
79
80 /** Integration direction. */
81 private boolean forward;
82
83 /** Variation direction around pending event.
84 * (this is considered with respect to the integration direction)
85 */
86 private boolean increasing;
87
88 /** Next action indicator. */
89 private EventHandler.Action nextAction;
90
91 /** Root-finding algorithm to use to detect state events. */
92 private final UnivariateSolver solver;
93
94 /** Simple constructor.
95 * @param handler event handler
96 * @param maxCheckInterval maximal time interval between switching
97 * function checks (this interval prevents missing sign changes in
98 * case the integration steps becomes very large)
99 * @param convergence convergence threshold in the event time search
100 * @param maxIterationCount upper limit of the iteration count in
101 * the event time search
102 * @param solver Root-finding algorithm to use to detect state events
103 */
104 public EventState(final EventHandler handler, final double maxCheckInterval,
105 final double convergence, final int maxIterationCount,
106 final UnivariateSolver solver) {
107 this.handler = handler;
108 this.maxCheckInterval = maxCheckInterval;
109 this.convergence = JdkMath.abs(convergence);
110 this.maxIterationCount = maxIterationCount;
111 this.solver = solver;
112
113 // some dummy values ...
114 expandable = null;
115 t0 = Double.NaN;
116 g0 = Double.NaN;
117 g0Positive = true;
118 pendingEvent = false;
119 pendingEventTime = Double.NaN;
120 previousEventTime = Double.NaN;
121 increasing = true;
122 nextAction = EventHandler.Action.CONTINUE;
123 }
124
125 /** Get the underlying event handler.
126 * @return underlying event handler
127 */
128 public EventHandler getEventHandler() {
129 return handler;
130 }
131
132 /** Set the equation.
133 * @param expandable equation being integrated
134 */
135 public void setExpandable(final ExpandableStatefulODE expandable) {
136 this.expandable = expandable;
137 }
138
139 /** Get the maximal time interval between events handler checks.
140 * @return maximal time interval between events handler checks
141 */
142 public double getMaxCheckInterval() {
143 return maxCheckInterval;
144 }
145
146 /** Get the convergence threshold for event localization.
147 * @return convergence threshold for event localization
148 */
149 public double getConvergence() {
150 return convergence;
151 }
152
153 /** Get the upper limit in the iteration count for event localization.
154 * @return upper limit in the iteration count for event localization
155 */
156 public int getMaxIterationCount() {
157 return maxIterationCount;
158 }
159
160 /** Reinitialize the beginning of the step.
161 * @param interpolator valid for the current step
162 * @exception MaxCountExceededException if the interpolator throws one because
163 * the number of functions evaluations is exceeded
164 */
165 public void reinitializeBegin(final StepInterpolator interpolator)
166 throws MaxCountExceededException {
167
168 t0 = interpolator.getPreviousTime();
169 interpolator.setInterpolatedTime(t0);
170 g0 = handler.g(t0, getCompleteState(interpolator));
171 if (g0 == 0) {
172 // excerpt from MATH-421 issue:
173 // If an ODE solver is setup with an EventHandler that return STOP
174 // when the even is triggered, the integrator stops (which is exactly
175 // the expected behavior). If however the user wants to restart the
176 // solver from the final state reached at the event with the same
177 // configuration (expecting the event to be triggered again at a
178 // later time), then the integrator may fail to start. It can get stuck
179 // at the previous event. The use case for the bug MATH-421 is fairly
180 // general, so events occurring exactly at start in the first step should
181 // be ignored.
182
183 // extremely rare case: there is a zero EXACTLY at interval start
184 // we will use the sign slightly after step beginning to force ignoring this zero
185 final double epsilon = JdkMath.max(solver.getAbsoluteAccuracy(),
186 JdkMath.abs(solver.getRelativeAccuracy() * t0));
187 final double tStart = t0 + 0.5 * epsilon;
188 interpolator.setInterpolatedTime(tStart);
189 g0 = handler.g(tStart, getCompleteState(interpolator));
190 }
191 g0Positive = g0 >= 0;
192 }
193
194 /** Get the complete state (primary and secondary).
195 * @param interpolator interpolator to use
196 * @return complete state
197 */
198 private double[] getCompleteState(final StepInterpolator interpolator) {
199
200 final double[] complete = new double[expandable.getTotalDimension()];
201
202 expandable.getPrimaryMapper().insertEquationData(interpolator.getInterpolatedState(),
203 complete);
204 int index = 0;
205 for (EquationsMapper secondary : expandable.getSecondaryMappers()) {
206 secondary.insertEquationData(interpolator.getInterpolatedSecondaryState(index++),
207 complete);
208 }
209
210 return complete;
211 }
212
213 /** Evaluate the impact of the proposed step on the event handler.
214 * @param interpolator step interpolator for the proposed step
215 * @return true if the event handler triggers an event before
216 * the end of the proposed step
217 * @exception MaxCountExceededException if the interpolator throws one because
218 * the number of functions evaluations is exceeded
219 * @exception NoBracketingException if the event cannot be bracketed
220 */
221 public boolean evaluateStep(final StepInterpolator interpolator)
222 throws MaxCountExceededException, NoBracketingException {
223
224 try {
225 forward = interpolator.isForward();
226 final double t1 = interpolator.getCurrentTime();
227 final double dt = t1 - t0;
228 if (JdkMath.abs(dt) < convergence) {
229 // we cannot do anything on such a small step, don't trigger any events
230 return false;
231 }
232 final int n = JdkMath.max(1, (int) JdkMath.ceil(JdkMath.abs(dt) / maxCheckInterval));
233 final double h = dt / n;
234
235 final UnivariateFunction f = new UnivariateFunction() {
236 /** {@inheritDoc} */
237 @Override
238 public double value(final double t) throws LocalMaxCountExceededException {
239 try {
240 interpolator.setInterpolatedTime(t);
241 return handler.g(t, getCompleteState(interpolator));
242 } catch (MaxCountExceededException mcee) {
243 throw new LocalMaxCountExceededException(mcee);
244 }
245 }
246 };
247
248 double ta = t0;
249 double ga = g0;
250 for (int i = 0; i < n; ++i) {
251
252 // evaluate handler value at the end of the substep
253 final double tb = (i == n - 1) ? t1 : t0 + (i + 1) * h;
254 interpolator.setInterpolatedTime(tb);
255 final double gb = handler.g(tb, getCompleteState(interpolator));
256
257 // check events occurrence
258 if (g0Positive ^ (gb >= 0)) {
259 // there is a sign change: an event is expected during this step
260
261 // variation direction, with respect to the integration direction
262 increasing = gb >= ga;
263
264 // find the event time making sure we select a solution just at or past the exact root
265 final double root;
266 if (solver instanceof BracketedUnivariateSolver<?>) {
267 @SuppressWarnings("unchecked")
268 BracketedUnivariateSolver<UnivariateFunction> bracketing =
269 (BracketedUnivariateSolver<UnivariateFunction>) solver;
270 root = forward ?
271 bracketing.solve(maxIterationCount, f, ta, tb, AllowedSolution.RIGHT_SIDE) :
272 bracketing.solve(maxIterationCount, f, tb, ta, AllowedSolution.LEFT_SIDE);
273 } else {
274 final double baseRoot = forward ?
275 solver.solve(maxIterationCount, f, ta, tb) :
276 solver.solve(maxIterationCount, f, tb, ta);
277 final int remainingEval = maxIterationCount - solver.getEvaluations();
278 BracketedUnivariateSolver<UnivariateFunction> bracketing =
279 new PegasusSolver(solver.getRelativeAccuracy(), solver.getAbsoluteAccuracy());
280 root = forward ?
281 UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
282 baseRoot, ta, tb, AllowedSolution.RIGHT_SIDE) :
283 UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
284 baseRoot, tb, ta, AllowedSolution.LEFT_SIDE);
285 }
286
287 if (!Double.isNaN(previousEventTime) &&
288 JdkMath.abs(root - ta) <= convergence &&
289 JdkMath.abs(root - previousEventTime) <= convergence) {
290 // we have either found nothing or found (again ?) a past event,
291 // retry the substep excluding this value, and taking care to have the
292 // required sign in case the g function is noisy around its zero and
293 // crosses the axis several times
294 do {
295 ta = forward ? ta + convergence : ta - convergence;
296 ga = f.value(ta);
297 } while ((g0Positive ^ (ga >= 0)) && (forward ^ (ta >= tb)));
298
299 if (forward ^ (ta >= tb)) {
300 // we were able to skip this spurious root
301 --i;
302 } else {
303 // we can't avoid this root before the end of the step,
304 // we have to handle it despite it is close to the former one
305 // maybe we have two very close roots
306 pendingEventTime = root;
307 pendingEvent = true;
308 return true;
309 }
310 } else if (Double.isNaN(previousEventTime) ||
311 JdkMath.abs(previousEventTime - root) > convergence) {
312 pendingEventTime = root;
313 pendingEvent = true;
314 return true;
315 } else {
316 // no sign change: there is no event for now
317 ta = tb;
318 ga = gb;
319 }
320 } else {
321 // no sign change: there is no event for now
322 ta = tb;
323 ga = gb;
324 }
325 }
326
327 // no event during the whole step
328 pendingEvent = false;
329 pendingEventTime = Double.NaN;
330 return false;
331 } catch (LocalMaxCountExceededException lmcee) {
332 throw lmcee.getException();
333 }
334 }
335
336 /** Get the occurrence time of the event triggered in the current step.
337 * @return occurrence time of the event triggered in the current
338 * step or infinity if no events are triggered
339 */
340 public double getEventTime() {
341 return pendingEvent ?
342 pendingEventTime :
343 (forward ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY);
344 }
345
346 /** Acknowledge the fact the step has been accepted by the integrator.
347 * @param t value of the independent <i>time</i> variable at the
348 * end of the step
349 * @param y array containing the current value of the state vector
350 * at the end of the step
351 */
352 public void stepAccepted(final double t, final double[] y) {
353
354 t0 = t;
355 g0 = handler.g(t, y);
356
357 if (pendingEvent && JdkMath.abs(pendingEventTime - t) <= convergence) {
358 // force the sign to its value "just after the event"
359 previousEventTime = t;
360 g0Positive = increasing;
361 nextAction = handler.eventOccurred(t, y, increasing == forward);
362 } else {
363 g0Positive = g0 >= 0;
364 nextAction = EventHandler.Action.CONTINUE;
365 }
366 }
367
368 /** Check if the integration should be stopped at the end of the
369 * current step.
370 * @return true if the integration should be stopped
371 */
372 public boolean stop() {
373 return nextAction == EventHandler.Action.STOP;
374 }
375
376 /** Let the event handler reset the state if it wants.
377 * @param t value of the independent <i>time</i> variable at the
378 * beginning of the next step
379 * @param y array were to put the desired state vector at the beginning
380 * of the next step
381 * @return true if the integrator should reset the derivatives too
382 */
383 public boolean reset(final double t, final double[] y) {
384
385 if (!(pendingEvent && JdkMath.abs(pendingEventTime - t) <= convergence)) {
386 return false;
387 }
388
389 if (nextAction == EventHandler.Action.RESET_STATE) {
390 handler.resetState(t, y);
391 }
392 pendingEvent = false;
393 pendingEventTime = Double.NaN;
394
395 return nextAction == EventHandler.Action.RESET_STATE ||
396 nextAction == EventHandler.Action.RESET_DERIVATIVES;
397 }
398
399 /** Local wrapper to propagate exceptions. */
400 private static final class LocalMaxCountExceededException extends RuntimeException {
401
402 /** Serializable UID. */
403 private static final long serialVersionUID = 20120901L;
404
405 /** Wrapped exception. */
406 private final MaxCountExceededException wrapped;
407
408 /** Simple constructor.
409 * @param exception exception to wrap
410 */
411 LocalMaxCountExceededException(final MaxCountExceededException exception) {
412 wrapped = exception;
413 }
414
415 /** Get the wrapped exception.
416 * @return wrapped exception
417 */
418 public MaxCountExceededException getException() {
419 return wrapped;
420 }
421 }
422 }